1. What is Critical Angle?

The critical angle is the minimum angle of incidence at which light is totally reflected at the boundary between two media with different refractive indices. It occurs when light travels from a medium with higher refractive index (n₁) to one with lower refractive index (n₂).

2. How Does the Calculator Work?

The calculator uses the critical angle formula:

Where:

• \( c \) — Critical angle (degrees)
• \( n_1 \) — Refractive index of first medium (higher index)
• \( n_2 \) — Refractive index of second medium (lower index)

Explanation: The arcsin function calculates the angle whose sine is the ratio of n₂ to n₁. Total internal reflection occurs when the angle of incidence exceeds this critical angle.

3. Importance of Critical Angle

Details: Critical angle is fundamental in fiber optics, prism design, and understanding optical phenomena like mirages. It determines the conditions for total internal reflection.

4. Using the Calculator

Tips: Enter both refractive indices (n₁ > n₂). n₁ must be greater than n₂ for a real critical angle to exist. Typical values: ~1.0 for air, ~1.33 for water, ~1.5 for glass.

5. Frequently Asked Questions (FAQ)

Q1: What happens if n₁ ≤ n₂?
A: No critical angle exists in this case. Light will refract but not undergo total internal reflection.

Q2: How does critical angle relate to fiber optics?
A: Fiber optics rely on total internal reflection, which occurs when light hits the core-cladding interface at angles greater than the critical angle.

Q3: What's the critical angle for water to air?
A: With n₁=1.33 (water) and n₂=1.0 (air), the critical angle is approximately 48.6°.

Q4: Does critical angle depend on wavelength?
A: Yes, since refractive index varies with wavelength (dispersion), the critical angle is slightly wavelength-dependent.

Q5: Can critical angle be greater than 90°?
A: No, by definition the critical angle must be between 0° and 90°.